# Copyright: Public domain. # Filename: CONIC_SUBROUTINES.agc # Purpose: Part of the source code for Colossus 2A, AKA Comanche 055. # It is part of the source code for the Command Module's (CM) # Apollo Guidance Computer (AGC), for Apollo 11. # Assembler: yaYUL # Contact: Ron Burkey . # Website: www.ibiblio.org/apollo. # Pages: 1262-1308 # Mod history: 2009-05-08 RSB Adapted from the Colossus249/ file of the # same name, using Comanche055 page images. # 2009-05-20 RSB Corrected: Fixed four interpreter # instructions. # # This source code has been transcribed or otherwise adapted from digitized # images of a hardcopy from the MIT Museum. The digitization was performed # by Paul Fjeld, and arranged for by Deborah Douglas of the Museum. Many # thanks to both. The images (with suitable reduction in storage size and # consequent reduction in image quality as well) are available online at # www.ibiblio.org/apollo. If for some reason you find that the images are # illegible, contact me at info@sandroid.org about getting access to the # (much) higher-quality images which Paul actually created. # # Notations on the hardcopy document read, in part: # # Assemble revision 055 of AGC program Comanche by NASA # 2021113-051. 10:28 APR. 1, 1969 # # This AGC program shall also be referred to as # Colossus 2A # Page 1262 # PROGRAM DESCRIPTION -- ENTIRE CONIC SUBROUTINE LOG SECTION DATE -- 1 SEPTEMBER 1967 # MOD NO. -- 0 LOG SECTION -- CONIC SUBROUTINES # MOD BY KRAUSE ASSEMBLY -- COLOSSUS REVISION 88 # # FUNCTIONAL DESCRIPTION -- # THE FOLLOWING SET OF SUBROUTINES SOLVE VARIOUS PROBLEMS INVOLVING THE TRAJECTORY PRODUCED BY A CENTRAL # INVERSE-SQUARE FORCE ACTING ON A POINT MASS, AS OUTLINED IN THE CMC AND LGC LUNAR LANDING MISSION GSOP, SECTION # 5.5.1.2. A GENERAL USAGE POINT-OF-VIEW WAS TAKEN IN FORMULATING, MECHANIZING, AND SCALING THE SUBROUTINES, # RATHER THAN OPTIMIZING EACH FOR A PARTICULAR USE. THEREFORE, MULTIPLE USAGE CAN BE MADE OF THE SUBROUTINES # INVOLVING ANY REALISTIC SET OF CONSTRAINTS. IT SHOULD BE NOTED THAT ONLY ONE SET OF CODING IS USED, WHETHER THE # EARTH, MOON, OR ANY OTHER CELESTIAL BODY IS SPECIFIED AS THE CENTRAL BODY OF THE PROBLEM, PROVIDED ONE OBSERVES # THE INHERENT SCALE CHANGE REQUIRED IN POSITION, VELOCITY, MU, AND TIME, AS OUTLINES IN MISSION PROGRAMMING # DEFINITION MEMO NO. 10. THIS CAN BE ACCOMPLISHED BY SIMPLY ADDING TO THE MUTABLE AND INITIALIZING THE SUBROUTINES # APPROPRIATELY. # # DUE TO THE UNIFORMITY OF THE EQUATIONS INVOLVED, CODING WAS MINIMIZED BY TREATING INDIVIDUAL EQUATIONS AND # BLOCKS OF EQUATIONS AS SUBROUTINES OF LOWER RANK WHENEVER POSSIBLE. AS A RESULT, THREE BY-PRODUCTS SUBROUTINES, # DIRECTLY USABLE AS INDEPENDENT SUBROUTINES, WERE GENERATED. # # RESTRICTIONS -- # THE ONLY LIMITATION IN THE SCOPE OF THE PROBLEM WHICH CAN BE SOLVED BY A PARTICULAR SUBROUTINE IS THE SCALING # LIMIT OF EACH PARAMETER AS SPECIFIED IN THE GSOP. THESE SCALING LIMITS WERE CHOSEN SO THAT ALL FEASIBLE TRAJECTORIES # COULD BE HANDLED. # # SINCE THE SUBROUTINES (EXCEPT KEPLER) USE COMMON SUBROUTINES OF LOWER RANK WHICH USE ERASABLE OTHER THAN # THE PUSHLIST (DUE TO ITS LIMITED SIZE) AND COMMON INTERPRETIVE SWITCHES, THE CONIC SUBROUTINES CANNOT BE ALLOWED # TO INTERRUPT EACH OTHER. IT IS UP TO THE USER TO GUARANTEE THIS CONDITION. # Page 1263 # PROGRAM DESCRIPTION -- KEPLER SUBROUTINE DATE -- 11 OCTOBER 1967 # MOD NO. -- 1 LOG SECTION -- CONIC SUBROUTINES # MOD BY KRAUSE ASSEMBLY -- COLOSSUS 103 AND SUNDANCE 222 # MOD NO. -- 2 (AUGUST 1968) BY ROBERTSON: TO PERMIT BACKDATING BY MORE THAN ONE ORBITAL PERIOD. # MOD NO. -- 3 (DEC 1968) BY ROBERTSON: SUPPRESSION OF X-MODULO-ING # MOD NO. -- 4 (JAN 1969) BY ROBERTSON: CLEAR OVFIND AT KEPLER ENTRY # # FUNCTIONAL DESCRIPTION -- # THIS SUBROUTINE, GIVEN AN INITIAL STATE VECTOR AND THE DESIRED TRANSFER TIME THROUGH WHICH THE STATE IS TO # BE UPDATED ALONG A CONIC TRAJECTORY, COMPUTES THE NEW, UPDATED STATE VECTOR. THE TRAJECTORY MAY BE ANY CONIC # SECTION -- CIRCULAR, ELLIPTIC, PARABOLIC, HYPERBOLIC, OR RECTILINEAR WITH RESPECT TO THE EARTH OR THE MOON. THE # USE OF THE SUBROUTINE CAN BE EXTENDED USING OTHER PRIMARY BODIES BY SIMPLE ADDITIONS TO THE MUTABLE WITHOUT # INTRODUCING ANY CODING CHANGES, ACCEPTING THE INHERENT SCALE FACTOR CHANGES IN POSITION AND VELOCITY. AN ITERATION # TECHNIQUE IS UTILIZED IN THE COMPUTATION. # # IF A NEGATIVE TIME-OF-FLIGHT IS INPUT, THE PROGRAM WILL SOLVE FOR THE STATE WHICH WOULD BE PRODUCED BY # EXTRAPOLATING THE POSITION BACKWARD IN TIME. # # IF THE ABSOLUTE VALUE DESIRED TRANSFER TIME EXCEEDS THE ORBITAL PERIOD, THE SUBROUTINE, THROUGH A # MODULAR TECHNIQUE, WILL COMPUTE THE STATE CORRESPONDING TO THE DESIRED TIME AS USUAL. # # THE RESTRICTIONS ARE -- # 1. (PREVIOUS RESTRICTION ON THE NEGATIVE DESIRED TRANSFER TIME IS NOW DELETED.) # 2. THE PARAMETERS IN THE PROBLEM CANNOT EXCEED THEIR SCALING LIMITS AS SPECIFIED IN THE GSOP. IF # ANY OF THESE LIMITS ARE EXCEEDED, THE RESULTING SOLUTION WILL BE MEANINGLESS. # # THE NUMBER OF ITERATIONS AND, THEREFORE, THE COMPUTATION SPEED IS DEPENDENT ON THE ACCURACY OF THE # GUESS, XKFPNEW. THE AGC COMPUTATION TIME IS APPROXIMATELY .061 SECONDS FOR INITIALIZATION, .065 SECONDS FOR THE # FINAL COMPUTATIONS, PLUS .083 SECONDS FOR EACH ITERATION. # # REFERENCES -- # R-479, MISSION PROGRAMMING DEFINITION MEMO NO. 10, LUNAR LANDING MISSION GSOP, SECTION 5.5, SGA # MEMO 67-4. # # INPUT -- ERASABLE INITIALIZATION REQUIRED # SCALE FACTOR # VARIABLE IN POWERS OF 2 DESCRIPTION AND REMARKS # -------- -------------- ----------------------- # RRECT +29 FOR EARTH DP INITIAL POSITION VECTOR IN METERS # +27 FOR MOON # Page 1264 # VRECT +7 FOR EARTH DP INITIAL VELOCITY VECTOR IN METERS/CENTISECOND # +5 FOR MOON # X1 (38D) NONE INDEX REGISTER SET TO -2D OR -10D ACCORDING TO WHETHER THE EARTH OR MOON, # RESPECTIVELY, IS THE CENTRAL BODY # TAU +28 DESIRED TRANSFER TIME IN CENTISECONDS (DP) # MAY BE POS OR NEG AND ABSOLUTE VALUE MAY BE GREATER OR LESS THAN ONE ORBITAL PERIOD. # XKEPNEW +17 FOR EARTH DP GUESS OF ROOT X OF KEPLERS EQN IN SQRT(METERS).SIGN SHOULD AGREE WITH THAT OF TAU. # +16 FOR MOON AND ABS VALUE SHOULD BE LESS THAN THAT CORRESPONDING TO A PERIOD, VIZ, 2PI SQRT(SEMI- # MAJOR AXIS), FOR SPEED OF CONVERGENCE, BUT IF EITHER CONDITION FAILS, XKEPNEW IS RESET # BY KEPLER TO A POOR BUT VALID GUESS. # TC +28 DP PREV. VALUE OF TIME IN CENTISECS. MUST BE LESS THAN ONE ORBITAL PERIOD. # XPREV +17 FOR EARTH DP PREV. VALUE OF X IN SQRT(METERS). MUST BE LESS THAN AN X CORRESPONDING TO ONE # +16 FOR MOON ORBITAL PERIOD, VIZ, 2PI SQRT(SEMI-MAJOR AXIS) # # SUBROUTINES CALLED -- # DELTIME # # CALLING SEQUENCE AND NORMAL EXIT MODES -- # KEPRTN-2 GOTO # MUST BE IN INTERPRETIVE MODE BUT OVFIND ARBITRARY. # KEPRTN-1 KEPLER # RETURNS WITH XPREV IN MPAC. PL IS AT 0. # KEPRTN ... # CONTINUE # # KEPLER MUST NOT BE CALLED DIRECTLY SINCE AN INTERRUPTION OF IT WOULD DESTROY THE ERASABLES IT NEEDS TO COMPLETE # THE INTERRUPTED JOB. THEREFORE THE USER MUST CALL CSMCONIC OR LEMCONIC WHICH GUARANTEES NO INTERRUPTS AND WHICH # ALSO CALLS KEPPREP TO COMPUTE A GUESS OF XKEPNEW. # # ABORT EXIT MODE -- # NONE # # OUTPUT -- # SCALE FACTOR # VARIABLE IN POWERS OF 2 DESCRIPTION AND REMARKS # -------- -------------- ----------------------- # RCV +29 FOR EARTH DP TERMINAL POSITION VECTOR IN METERS # +27 FOR MOON # VCV +7 FOR EARTH DP TERMINAL VELOCITY VECTOR IN METERS/CENTISEC # +5 FOR MOON # TC +28 DP TRANSFER TIME IN CENTISECS TO WHICH KEPLER CONVERGED. ALWAYS LESS THAN ONE PERIOD. # XPREV +17 FOR EARTH DP VALUE OF X IN SQRT(METERS) TO WHICH KEPLER CONVERGED. ALWAYS LESS THAN THE X # +16 FOR MOON CORRESPONDING TO ONE PERIOD. # Page 1265 # FOR OTHER OUTPUT WHICH MAY BE OF USE, SEE DEBRIS. # # DEBRIS -- # PARAMETERS WHICH MAY BE OF USE -- # SCALE FACTOR # VARIABLE IN POWERS OF 2 DESCRIPTION AND REMARKS # -------- -------------- ----------------------- # URRECT +1 DP UNIT VECTOR OF INITIAL POSITION # R1 +29 FOR EARTH DP MAGNITUDE OF INITIAL POSITION IN METERS # +27 FOR MOON # ALPHA -22 FOR EARTH DP INVERSE OF SEMI-MAJOR AXIS IN 1/METERS # -20 FOR MOON # TMODULO +28 DP INTEGRAL NUMBER OF PERIODS IN CENTISECS, WHICH WAS SUBTRACTED FROM TAU. TO PRODUCE A # TAU. OF LESS THAN ONE PERIOD. # # PARAMETERS OF NO USE -- # DP PARAMETERS -- FPSILENT, DELX, DELT, RCNORM, XMODULO, PLUS PUSHLIST REGISTERS 0 THROUGH 39D. # Page 1266 # PROGRAM DESCRIPTION -- LAMBERT SUBROUTINE DATE -- 1 SEPTEMBER 1967 # MOD NO. -- 0 LOG SECTION -- CONIC SUBROUTINES # MOD BY KRAUSE ASSEMBLY -- COLOSSUS REVISION 88 # # FUNCTIONAL DESCRIPTION -- # THIS SUBROUTINE CALCULATES THE INITIAL VELOCITY REQUIRED TO TRANSFER A POINT-MASS ALONG A CONIC TRAJECTORY # FROM AN INITIAL POSITION TO A TERMINAL POSITION IN A PRESCRIBED TIME INTERVAL. THE RESULTING TRAJECTORY MAY BE # A SECTION OF A CIRCLE, ELLIPSE, PARABOLA, OR HYPERBOLA WITH RESPECT TO THE EARTH OR THE MOON. THE USE OF THE # SUBROUTINE CAN BE EXTENDED USING OTHER PRIMARY BODIES BY SIMPLE ADDITIONS TO THE MUTABLE WITHOUT INTRODUCING ANY # CODING CHANGES, ACCEPTING THE INHERENT SCALE FACTOR CHANGES IN POSITION AND VELOCITY. AN ITERATION TECHNIQUE IS # UTILIZED IN THE COMPUTATION. # # THE RESTRICTIONS ARE: -- # 1. RECTILINEAR TRAJECTORIES CANNOT BE COMPUTED. # 2. AN ACCURACY DEGRADATION OCCURS AS THE COSINE OF THE TRUE ANOMALY DIFFERENCE APPROACHES +1.0. # 3. THE ANGLE BETWEEN ANY POSITION VECTOR AND ITS VELOCITY VECTOR MUST BE GREATER THAN 1 DEGREE 47.5 MINUTES # AND LESS THAN 178 DEGREES 12.5 MINUTES. # 4. NEGATIVE TRANSFER TIME IS AMBIGUOUS AND WILL RESULT IN NO SOLUTION. # 5. THE PARAMETERS IN THE PROBLEM MUST NOT EXCEED THEIR SCALING LIMITS SPECIFIED IN THE GSOP. IF THE # LIMITS ARE EXCEEDED, THE RESULTING SOLUTION WILL BE MEANINGLESS. # # THE NUMBER OF ITERATIONS AND, THEREFORE, THE COMPUTATION'S SPEED IS DEPENDENT ON THE ACCURACY OF THE FIRST # GUESS OF THE INDEPENDENT VARIABLE, COGA. THE AGC COMPUTATION TIME IS APPROXIMATELY # .105 SECONDS FOR INITIALIZATION, .069 SECONDS FOR FINAL COMPUTATIONS, PLUS .205 SECONDS FOR EACH ITERATION. # # REFERENCES -- # R-479, MISSION PROGRAMMING DEFINITION MEMO NO. 10, LUNAR LANDING MISSION GSOP -- SECTION 5.5, SGA MEMO 67-8, # SGA MEMO 67-4. # # INPUT -- ERASABLE INITIALIZATION REQUIRED # SCALE FACTOR # VARIABLE IN POWERS OF 2 DESCRIPTION AND REMARKS # -------- -------------- ----------------------- # R1VEC +29 FOR EARTH DP INITIAL POSITION VECTOR IN METERS # +27 FOR MOON # R2VEC +29 FOR EARTH DP TARGET OR TERMINAL POSITION VECTOR IN METERS # +27 FOR MOON # TDESIRED +28 DP DESIRED TRANSFER TIME IN CENTISECONDS # X1 (38D) NONE INDEX REGISTER SET TO -2D OR -10D ACCORDING TO WHETHER THE EARTH OR MOON, # RESPECTIVELY, IS THE CENTRAL BODY # GEOMSGN NONE SP +.5 IF DESIRED TRANSFER ANGLE IS LESS THAN 180 DEGREES, -.5 IF GREATER THAN 180 DEG. # GUESSW NONE AN INTERPRETER SWITCH TO BE SET IF NO GUESS OF COGA IS AVAILABLE, CLEAR IF A GUESS OF # Page 1267 # COGA IS TO BE USED BY LAMBERT # COGA +5 DP GUESS OF COTANGENT OF FLIGHT PATH ANGLE (MEASURED FROM VERTICAL). THIS WILL BE # IGNORED IF GUESSW IS SET. # NORMSW NONE AN INTERPRETER SWITCH TO BE SET IF UN IS TO BE AN INPUT TO THE SUBROUTINE, CLEAR IF # LAMBERT IS TO COMPUTE ITS OWN NORMAL (UN). # UN +1 DP UNIT NORMAL TO THE DESIRED ORBIT PLANE IN THE DIRECTION OF THE RESULTING ANGULAR # MOMENTUM VECTOR. THIS WILL BE IGNORED IF NORMSW IS CLEAR. # VTARGTAG NONE A S.P. TAG TO BE SET TO ZERO IF LAMBERT IS TO COMPUTE THE VELOCITY OF R2VEC AS WELL AS # AT R1VEC. # # SUBROUTINES CALLED -- # GEOM, GETX, DELTIME, ITERATOR, LAMENTER (PART OF NEWSTATE) # # CALLING SEQUENCE AND NORMAL EXIT MODES -- # L CALL # MUST BE IN INTERPRETIVE MODE BUT OVFIND ARBITRARY. # L+1 LAMBERT # RETURNS WITH PL AT 0 AND WITH VVEC IN MPAC IF VTARGTAG WAS WAS NON-ZERO OR VTARGET # # IN MPAC IF VTARGTAG WAS ZERO # L+2 BON # CONTINUE IF SOLNSW CLEAR SINCE SOLUTION IS ACCEPTABLE # L+3 SOLNSW # L+4 LAMABORT # # IF A LAMBER RESULT IS TO BE A FIRST GUESS FOR THE NEXT LAMBERT CALCULATION, COGA MUST BE PRESERVED AND # GUESSW MUST BE CLEAR FOR EACH SUCCEEDING LAMBERT CALL. # # ABORT EXIT MODES -- # IF SOLNSW WAS SET UPON EXITING, EITHER LAMBERT WAS ASKED TO COMPUTE A TRANSFER TOO NEAR 0 OR 360 DEG, OR T # WAS TOO SMALL TO PRODUCE A REALISTIC TRANSFER BETWEEN R1VEC AND R2FEC. IN EITHER CASE THE FIX MUST BE MADE # ACCORDING TO THE NEEDS OF THE PARTICULAR USER. THE ABORT EXIT MODE MAY BE CODED AS ... # LAMBERT DLOAD ABS # A MEASURE OF THE PROXIMITY TO 0 OR # 1-CHTH # 360 DEGREES. # DSU BWM # ONEBIT # CHANGER2 # CHANGE R2VEC DIRECTION SLIGHTLY. # DLOAD DAD # TDESIRED # SOMETIME # STCALL TDESIRED # INCRESE TDESIRED # LAMBERT # # OUTPUT -- # SCALE FACTOR # VARIABLE IN POWERS OF 2 DESCRIPTION AND REMARKS # Page 1268 # -------- -------------- ----------------------- # VVEC +7 FOR EARTH DP INITIAL VELOCITY VECTOR IN METERS/CENTISECOND REQUIRED TO SATISFY THE BOUNDARY VALUE # +5 FOR MOON PROBLEM. # VTARGET +7 FOR EARTH DP RESULTANT VELOCITY VECTOR AT R2VEC IN METERS/CENTISECOND. # +5 FOR MOON # SOLNSW NONE INTERPRETER SWITCH WHICH IS SET IF THE SUBROUTINE CANNOT SOLVE THE PROBLEM, CLEAR IF THE # SOLUTION EXISTS. # # FOR OTHER OUTPUT WHICH MAY BE OF USE, SEE DEBRIS. # # DEBRIS -- # PARAMETERS WHICH MAY BE OF USE -- # SCALE FACTOR # VARIABLE IN POWERS OF 2 DESCRIPTION AND REMARKS # -------- -------------- ----------------------- # SNTH +1 DP SIN OF ANGLE BETWEEN R1VEC AND R2VEC # CSTH +1 DP COSINE OF ANGLE # 1-CSTH +2 DP 1-CSTH # COGA +5 DP COTAN OF INITIAL REQUIRED FLIGHT PATH ANGLE MEASURED FROM VERTICAL # P +4 DP RATIO OF SEMILATUS RECTUM TO INITIAL RADIUS # R1A +6 DP RATIO OF INITIAL RADIUS TO SEMI-MAJOR AXIS # R1 (32D) +29 FOR EARTH DP INITIAL RADIUS IN METERS # +27 FOR MOON # UR1 +1 DP UNIT VECTOR OF R1VEC # U2 +1 DP UNIT VECTOR OF R2VEC # # PARAMETERS OF NO USE -- # DP PARAMETERS -- EPSILONL, CSTH-RHO, TPREV, TERRLAMB, R2, RTNLAMB (SP), PLUS PUSHLIST REGISTER 0 THROUGH 41D # ADDITIONAL INTERPRETIVE SWITCHES USED -- INFINFLG, 360SW, SLOPESW, ORDERSW # Page 1269 # PROGRAM DESCRIPTION -- TIME-THETA SUBROUTINE DATE -- 1 SEPTEMBER 1967 # MOD NO. -- 0 LOG SECTION -- CONIC SUBROUTINES # MOD BY KRAUSE ASSEMBLY -- COLOSSUS REVISION 88 # # FUNCTIONAL DESCRIPTION -- # THIS SUBROUTINE, GIVEN AN INITIAL STATE VECTOR AND A DESIRED TRUE-ANOMALY-DIFFERENCE THROUGH WHICH THE # STATE IS TO BE UPDATED ALONG A CONIC TRAJECTORY, CALCULATES THE CORRESPONDING TIME-OF-FLIGHT AND, IN ADDITION, # PROVIDES THE OPTION OF COMPUTING THE NEW UPDATED STATE VECTOR. THE RESULTING TRAJECTORY MAY BE A SECTION OF A # CIRCLE, ELLIPSE, PARABOLA, OR HYPERBOLA WITH RESPECT TO THE EARTH OR THE MOON. THE USE OF THE SUBROUTINE CAN BE # EXTENDED USING OTHER PRIMARY BODIES BY SIMPLE ADDITIONS TO THE MUTABLE WITHOUT INTRODUCING ANY CODING CHANGES, # ACCEPTING THE INHERENT SCALE FACTOR CHANGES IN POSITION AND VELOCITY. # # THE RESTRICTIONS ARE -- # 1. THE ANGLE BETWEEN ANY POSITION VECTOR AND ITS VELOCITY VECTOR MUST BE GREATER THAN 1 DEGREE 47.5 MINUTES # AND LESS THAN 178 DEGREES 12.5 MINUTES. # 2. THE PARAMETERS IN THE PROBLEM MUST NOT EXCEED THEIR SCALING LIMITS SPECIFIED IN THE GSCP. IF THE LIMITS # ARE EXCEEDED, THE RESULTING SOLUTION WILL BE MEANINGLESS. # # THE AGC COMPUTATION TIME IS APPROXIMATELY .292 SECONDS. # # REFERENCES -- # R-479, MISSION PROGRAMMING DEFINITION MEMO NO. 10, LUNAR LANDING MISSION GSOP-SECTION 5.5, SGA MEMO 67-8. # # INPUT -- ERASABLE INITIALIZATION REQUIRED # SCALE FACTOR # VARIABLE IN POWERS OF 2 DESCRIPTION AND REMARKS # -------- -------------- ----------------------- # RVEC +29 FOR EARTH DP INITIAL POSITION VECTOR IN METERS # +27 FOR MOON # VVEC +7 FOR EARTH DP INITIAL VELOCITY VECTOR IN METERS/CENTISECOND # +5 FOR MOON # SNTH +1 ` DP SINE OF THE TRUE-ANOMALY-DIFFERENCE THROUGH WHICH THE STATE IS TO BE UPDATED # CSTH +1 DP COSINE OF THE ANGLE # RVSW NONE AN INTERPRETIVE SWITCH TO BE SET IF ONLY TIME IS TO BE AN OUTPUT, CLEAR IF THE NEW STATE # IS TO BE COMPUTED ALSO. # X1 (38D) NONE INDEX REGISTER TO BE SET TO -2D OR -10D ACCORDING TO WHETHER THE EARTH OR MOON, # RESPECTIVELY, IS THE CENTRAL BODY. # # SUBROUTINES CALLED -- # Page 1270 # PARAM, GEOM, GETX, DELTIME, NEWSTATE # # CALLING SEQUENCE AND NORMAL EXIT MODES -- # IF ONLY TIME IS DESIRED AS OUTPUT -- # L SET CALL # MUST BE IN INTERPRETIVE MODE BUT OVFIND ARBITRARY. # L+1 RVSW # L+2 TIMETHET # RETURN WITH PL AT 0 AND T IN MPAC # L+3 ... # CONTINUE # # IF THE UPDATE STATE VECTOR IS DESIRED AS WELL -- # L CLEAR CALL # MUST BE IN INTERPRETIVE MODE BUT OVFIND ARBITRARY. # L+1 RVSW # L+2 TIMETHET # RETURNS WITH PL AT 6. THE INITIAL POSITION VECTOR IS IN 0D OF THE PUSHLIST AND # # THE INITIAL VELOCITY VECTOR IN MPAC. # L+3 STOVL NEWVVEC # L+4 STADR # L+5 STORE NEWRVEC # NEWVVEC AND NEWRVEC ARE SYMBOLIC REPRESENTATIONS OF THE USER'S LOCATIONS. # L+6 ... # CONTINUE. # # ABORT EXIT MODES -- # IF COGAFLAG AND/OR INFINFLG IS SET AT THE EXIT TO TIME-THETA, TIME-THETA WILL TRANSFER TO P00DOO WITH # AN ALARM CODE (ORIGINALLY 00607), AND NOT RETURN TO THE CALLING PROGRAM. (PCR 692 AND 721). # # OUTPUT -- # SCALE FACTOR # VARIABLE IN POWERS OF 2 DESCRIPTION AND REMARKS # -------- -------------- ----------------------- # T(30D) +28 DP TRANSFER TIME IN CENTISECONDS # INFINFLG NONE AN INTERPRETIVE SWITCH WHICH IS SET IF THE TRANSFER ANGLE REQUIRES CLOSURE THROUGH # INFINITY (NO SOLUTION), CLEAR IF A PHYSICAL SOLUTION IS POSSIBLE. # COGAFLAG NONE AN INTERPRETIVE SWITCH WHICH IS SET IF RESTRICTION 1 HAS BEEN VIOLATED (NO SOLUTION), # CLEAR IF NOT. # # IN ADDITION, IF RVSW IS CLEAR, THE FOLLOWING ARE OUTPUT -- # MPAC - +7 FOR EARTH DP TERMINAL VELOCITY VECTOR IN METERS/CENTISEC. # MPAC+5 +5 FOR MOON # 0D - 5D +29 FOR EARTH DP TERMINAL POSITION VECTOR IN METERS (PL AT 6D) # +27 FOR MOON # # FOR OTHER OUTPUT WHICH MAY BE OF USE, SEE DEBRIS. # Page 1271 # # DEBRIS -- # PARAMETERS WHICH MAY BE OF USE -- # SCALE FACTOR # VARIABLE IN POWERS OF 2 DESCRIPTION AND REMARKS # -------- -------------- ----------------------- # R1 (32D) +29 FOR EARTH DP MAGNITUDE OF INITIAL POSITION VECTOR, RVEC, IN METERS # +27 FOR MOON # R1A +6 DP RATIO OF R1 TO SEMI-MAJOR AXIS (NEG. FOR HYPERBOLIC TRAJECTORIES) # P +4 DP RATIO OF SEMILATUS RECTUM TO R1 # COGA +5 DP COTAN OF ANGLE BETWEEN RVEC AND VVEC # UR1 +1 DP UNIT VECTOR OF RVEC # U2 +1 DP UNIT VECTOR OF VVEC # UN +1 DP UNIT VECTOR OF UR1*U2 # # PARAMETERS OF NO USE -- # SP PARAMETERS -- RTNTT, GEOMSGN, RTNPRM, MAGVEC2=R2 (DP), PLUS PUSHLIST LOCATIONS 0-11D, 14D-21D, 24D-39D, 41D # ADDITIONAL INTERPRETIVE SWITCHES USED -- NORMSW, 360SW # Page 1272 # PROGRAM DESCRIPTION -- TIME-RADIUS SUBROUTINE DATE -- 11 OCTOBER 1967 # MOD NO. -1 LOG SECTION -- CONIC SUBROUTINES # MOD BY KRAUSE ASSEMBLY -- COLOSSUS REVISION 88 # # FUNCTIONAL DESCRIPTION -- # THIS SUBROUTINE, GIVEN AN INITIAL STATE VECTOR AND A DESIRED RADIUS TO WHICH THE # STATE IS TO BE UPDATED ALONG A CONIC TRAJECTORY, CALCULATES THE CORRESPONDING TIME-OF-FLIGHT AND, IN ADDITION, # PROVIDES THE OPTION OF COMPUTING THE NEW UPDATED STATE VECTOR. THE RESULTING TRAJECTORY MAY BE A SECTION OF A # CIRCLE, ELLIPSE, PARABOLA, OR HYPERBOLA WITH RESPECT TO THE EARTH OR THE MOON. THE USE OF THE SUBROUTINE CAN BE # EXTENDED USING OTHER PRIMARY BODIES BY SIMPLE ADDITIONS TO THE MUTABLE WITHOUT INTRODUCING ANY CODING CHANGES, # ACCEPTING THE INHERENT SCALE FACTOR CHANGES IN POSITION AND VELOCITY. # # IF THE DESIRED RADIUS IS BEYOND THE RADIUS OF APOCENTER OF THE CONIC OR BELOW THE RADIUS OF PERICENTER, # APSESW WILL BE SET AND THE SUBROUTINE WILL RETURN THE APOCENTER OR PERICENTER SOLUTION, RESPECTIVELY. # # THE RESTRICTIONS ARE -- # 1. THE ANGLE BETWEEN ANY POSITION VECTOR AND ITS VELOCITY VECTOR MUST BE GREATER THAN 1 DEGREE 47.5 MINUTES # AND LESS THAN 178 DEGREES 12.5 MINUTES. # 2. THE PARAMETERS IN THE PROBLEM MUST NOT EXCEED THEIR SCALING LIMITS SPECIFIED IN THE GSOP. IF THE LIMITS # EXCEEDED, THE RESULTING SOLUTION WILL BE MEANINGLESS. # 3. AN ACCURACY DEGRADATION OCCURS AS THE SENSITIVITIES OF TIME AND UPDATED STATE VECTOR TO CHANGES IN # RDESIRED INCREASE. THIS WILL OCCUR NEAR EITHER APSIS OF THE CONIC AND WHEN THE CONIC IS NEARLY CIRCULAR. IN # PARTICULAR, IF THE CONIC IS AN EXACT CIRCLE, THE PROBLEM IS UNDEFINED AND THE SUBROUTINE WILL ABORT. # # THE AGC COMPUTATION TIME IS APPROXIMATELY .363 SECONDS. # # REFERENCES -- # R-479, MISSION PROGRAMMING DEFINITION MEMO NO. 10, LUNAR LANDING MISSION GSOP-SECTION 5.5, SGA MEMO 67-8. # # INPUT -- ERASABLE INITIALIZATION REQUIRED. # SCALE FACTOR # VARIABLE IN POWERS OF 2 DESCRIPTION AND REMARKS # -------- -------------- ----------------------- # RVEC +29 FOR EARTH DP INITIAL POSITION VECTOR IN METERS # +27 FOR MOON # VVEC +7 FOR EARTH DP INITIAL VELOCITY VECTOR IN METERS/CENTISECOND # +5 FOR MOON # RDESIRED +29 FOR EARTH DP TERMINAL RADIAL DISTANCE ON CONIC TRAJECTORY FOR WHICH TRANSFER TIME IS TO BE # +27 FOR MOON COMPUTED # SGNRDOT NONE SP TAG SET TO +.5 OR -.5 ACCORDING TO WHETHER THE RADIAL VELOCITY AT RDESIRED IS TO BE # POSITIVE OR NEGATIVE, RESPECTIVELY. THIS TAG REDUCES THE DOUBLE-VALUED PROBLEM TO A # Page 1273 # SINGLE-VALUED PROBLEM. # X1 (38D) NONE INDEX REGISTER TO BE SET TO -2D OR -10D ACCORDING TO WHETHER THE EARTH OR MOON, # RESPECTIVELY, IS THE CENTRAL BODY. # RVSW NONE AN INTERPRETIVE SWITCH TO BE SET IF ONLY TIME IS TO BE AN OUTPUT, CLEAR IF THE NEW STATE # IS TO BE COMPUTED ALSO. # # SUBROUTINES CALLED -- # PARAM, GEOM, GETX, DELTIME, NEWSTATE # # CALLING SEQUENCE AND NORMAL EXIT MODES -- # IF ONLY TIME IS DESIRED AS OUTPUT -- # L SET CALL # MUST BE IN INTERPRETIVE MODE BUT OVFIND ARBITRARY. # L+1 RVSW # L+2 TIMERAD # RETURN WITH PL AT 0 AND T IN MPAC # L+3 ... # CONTINUE # # IF THE UPDATE STATE VECTOR IS DESIRED AS WELL -- # L CLEAR CALL # MUST BE IN INTERPRETIVE MODE BUT OVFIND ARBITRARY. # L+1 RVSW # L+2 TIMERAD # RETURNS WITH PL AT 6. THE INITIAL POSITION VECTOR IS IN 0D OF THE PUSHLIST AND # # THE INITIAL VELOCITY VECTOR IN MPAC. # L+3 STOVL NEWVVEC # L+4 STADR # L+5 STORE NEWRVEC # NEWVVEC AND NEWRVEC ARE SYMBOLIC REPRESENTATIONS OF THE USER'S LOCATIONS. # L+6 ... # CONTINUE # # ABORT EXIT MODES -- # IF SOLNSW AND/OR COGAFLAG AND/OR INFINFLG IS SET AT THE EXIT TO TIME-RADIUS, TIME-RADIUS WILL TRANSFER # TO P00DOO WITH AN ALARM CODE (ORIGINALLY 00607), AND NOT RETURN TO THE CALLING PROGRAM. (PCR 692 & 721). # # OUTPUT -- # SCALE FACTOR # VARIABLE IN POWERS OF 2 DESCRIPTION AND REMARKS # -------- -------------- ----------------------- # T (30D) +28 DP TRANSFER TIME IN CENTISECONDS. # INFINFLG NONE AN INTERPRETIVE SWITCH WHICH IS SET IF RDESIRED AND SGNRDOT REQUIRE CLOSURE THROUGH # INFINITY (NO SOLUTION), CLEAR IF A PHYSICAL SOLUTION IS POSSIBLE. # COGAFLAG NONE AN INTERPRETIVE SWITCH WHICH IS SET IF RESTRICTION 1 HAS BEEN VIOLATED (NO SOLUTION), # CLEAR IF NOT. # APSESW NONE AN INTERPRETIVE SWITCH WHICH IS SET IF RDESIRED WAS GREATER THAN RADIUS OF APOCENTER OR # Page 1274 # LESS THAN RADIUS OF PERICENTER. THE APOCENTER OR PERICENTER SOLUTION, RESPECTIVELY, # WILL THEN BE RETURNED. THE SWITCH IS CLEAR IF RDESIRED WAS BETWEEN PERICENTER AND # APOCENTER. # SOLNSW NONE AN INTERPRETIVE SWITCH WHICH IS SET IF THE CONIC IS SO CLOSE TO A CIRCLE THAT THE TERMIN # POINT IS AMBIGUOUS, VIOLATING RESTRICTION 3. IF ECCENTRICITY IS GREATER THAN 2-TO-THE- # MINUS-18, THE SWITCH IS CLEAR. # # IN ADDITION, IF RVSW IS CLEAR, THE FOLLOWING ARE OUTPUT -- # MPAC - +7 FOR EARTH DP TERMINAL VELOCITY VECTOR IN METERS/CENTISEC. # MPAC+5 +5 FOR MOON # 0D - 5D +29 FOR EARTH DP TERMINAL POSITION VECTOR IN METERS (PL AT 6D) # +27 FOR MOON # # FOR OTHER OUTPUT WHICH MAY BE OF USE, SEE DEBRIS. # # DEBRIS -- # PARAMETERS WHICH MAY BE OF USE -- # SCALE FACTOR # VARIABLE IN POWERS OF 2 DESCRIPTION AND REMARKS # -------- -------------- ----------------------- # R1 (32D) +29 FOR EARTH DP MAGNITUDE OF INITIAL POSITION VECTOR, RVEC, IN METERS # +27 FOR MOON # R1A +6 DP RATIO OF R1 TO SEMI-MAJOR AXIS (NEG. FOR HYPERBOLIC TRAJECTORIES) # P +4 DP RATIO OF SEMILATUS RECTUM TO R1 # COGA +5 DP COTAN OF ANGLE BETWEEN RVEC AND VVEC # UR1 +1 DP UNIT VECTOR OF RVEC # U2 +1 DP UNIT VECTOR OF VVEC # UN +1 DP UNIT VECTOR OF UR1*U2 # CSTH +1 DP COSINE OF TRUE ANOMALY DIFFERENCE BETWEEN RVEC AND RDESIRED. # SNTH +1 DP SINE OF TRUE ANOMALY DIFFERENCE. # # PARAMETERS OF NO USE -- # SP PARAMETERS -- RTNTT, GEOMSGN, RTNPRM, MAGVEC2*R2 (DP), PLUS PUSHLIST LOCATIONS 0-11D, 14D-21D, 24D-39D, 41D # ADDITIONAL INTERPRETIVE SWITCHES USED -- NORMSW, 360SW # # Page 1275 # PROGRAM DESCRIPTION -- APSIDES SUBROUTINE DATE -- 1 SEPTEMBER 1967 # MOD NO. -- 0 LOG SECTION -- CONIC SUBROUTINES # MOD BY KRAUSE ASSEMBLY -- COLOSSUS REVISION 88 # # FUNCTIONAL DESCRIPTION -- # THIS SUBROUTINE, GIVEN AN INITIAL STATE VECTOR, CALCULATES THE RADIUS OF PERICENTER AND OF APOCENTER AND THE # ECCENTRICITY OF THE RESULTING CONIC TRAJECTORY, WHICH MAY BE A STRAIGHT LINE, # CIRCLE, ELLIPSE, PARABOLA, OR HYPERBOLA WITH RESPECT TO THE EARTH OR THE MOON. THE USE OF THE SUBROUTINE CAN # BE EXTENDED USING OTHER PRIMARY BODIES BY SIMPLE ADDITIONS TO THE MUTABLE WITHOUT INTRODUCING ANY CODING CHANGES, # ACCEPTING THE INHERENT SCALE FACTOR CHANGES IN POSITION AND VELOCITY. # # THE RESTRICTIONS ARE -- # 1. IF APOCENTER IS BEYOND THE SCALING OF POSITION, THE SCALE FACTOR LIMIT (536,870,910 METERS WITH RESPECT # TO THE EARTH OR 134,217,727.5 METERS WITH RESPECT TO THE MOON) WILL BE RETURNED. # 2. THE PARAMETERS IN THE PROBLEM MUST NOT EXCEED THEIR SCALING LIMITS SPECIFIED IN THE GSOP. IF THE LIMITS # ARE EXCEEDED, THE RESULTING SOLUTION WILL BE MEANINGLESS. # # THE AGC COMPUTATION TIME IS APPROXIMATELY .103 SECONDS. # # REFERENCES -- # MISSION PROGRAMMING DEFINITION MEMO NO. 10, LUNAR LANDING MISSION GSOP-SECTION 5.5. # # INPUT -- ERASABLE INITIALIZATION REQUIRED # SCALE FACTOR # VARIABLE IN POWERS OF 2 DESCRIPTION AND REMARKS # -------- -------------- ----------------------- # RVEC +29 FOR EARTH DP INITIAL POSITION VECTOR IN METERS # +27 FOR MOON # VVEC +7 FOR EARTH DP INITIAL VELOCITY VECTOR IN METERS/CENTISECOND # +5 FOR MOON # X1 (38D) NONE INDEX REGISTER TO BE SET TO -2D OR -10D ACCORDING TO WHETHER THE EARTH OR MOON, # RESPECTIVELY, IS THE CENTRAL BODY. # # SUBROUTINES CALLED -- # PARAM, GEOM # # CALLING SEQUENCE AND NORMAL EXIT MODES -- # Page 1276 # IF ONLY TIME IS DESIRED AS OUTPUT -- # L CALL # MUST BE IN INTERPRETIVE MODE BUT OVFIND ARBITRARY. # L+1 APSIDES # RETURNS WITH PL AT 0, RADIUS OF APOCENTER IN MPAC AND RADIUS OF PERICENTER IN 0D # L+2 STODL APOAPSE # L+3 0D # L+4 STORE PERIAPSE # APOAPSE AND PERIAPSE ARE SYMBOLIC REPRESENTATIONS OF THE USER'S LOCATIONS # L+5 ... # CONTINUE # # OUTPUT -- # SCALE FACTOR # VARIABLE IN POWERS OF 2 DESCRIPTION AND REMARKS # -------- -------------- ----------------------- # MPAC +29 FOR EARTH DP RADIUS OF APOCENTER IN METERS # +27 FOR MOON # 0D-1D +29 FOR EARTH DP RADIUS OF PERICENTER IN METERS # +27 FOR MOON # ECC +3 DP ECCENTRICITY OF CONIC TRAJECTORY # # FOR OTHER OUTPUT WHICH MAY BE OF USE, SEE DEBRIS. # # DEBRIS -- # PARAMETERS WHICH MAY BE OF USE -- # SCALE FACTOR # VARIABLE IN POWERS OF 2 DESCRIPTION AND REMARKS # -------- -------------- ----------------------- # R1 (32D) +29 FOR EARTH DP MAGNITUDE OF INITIAL POSITION VECTOR, RVEC, IN METERS # +27 FOR MOON # R1A +6 DP RATIO OF R1 TO SEMI-MAJOR AXIS (NEG. FOR HYPERBOLIC TRAJECTORIES) # P +4 DP RATIO OF SEMILATUS RECTUM TO R1 # COGA +5 DP COTAN OF ANGLE BETWEEN RVEC AND VVEC # UR1 +1 DP UNIT VECTOR OF RVEC # U2 +1 DP UNIT VECTOR OF VVEC # UN +1 DP UNIT VECTOR OF UR1*U2 # MAGVEC2 +7 FOR EARTH DP MAGNITUDE OF VVEC # +5 FOR MOON # # PARAMETERS OF NO USE -- # SP PARAMETERS -- RTNAPSE, GOMSGN, RTNPRM, PLUS PUSHLIST LOCATIONS 0-5, 10D-11D, 14D-21D, 31D-38D. # ADDITIONAL INTERPRETIVE SWITCHES USED -- NORMSW SETLOC CONICS # Page 1277 BANK COUNT 12/CONIC EBANK= UR1 KEPLERN SETPD BOV 0 +1 VLOAD* MUTABLE,1 STOVL 14D RRECT UNIT SSP ITERCTR 20D STODL URRECT 36D STOVL R1 RRECT DOT SL1R VRECT DMP SL1R 1/ROOTMU # 1/ROOTMU (-17 OR -14) STOVL KEPC1 # C1=R.V/ROOTMU (+17 OR +16) VRECT VSQ DMPR 1/MU # 1/MU (-34 OR -28) DMP SL3 R1 DSU ROUND D1/64 STORE KEPC2 # C2=RV.V/MU -1 (+6) BDSU SR1R D1/64 DDV R1 STORE ALPHA # ALPHA=(1-C2)/R1 (-22 OR -20) BPL DLOAD # MAXIMUM X DEPENDS ON TYPE OF CONIC 1REV -50SC # -50SC (+12) DDV BOV ALPHA STOREMAX SQRT GOTO STOREMAX # Page 1278 1REV SQRT BDDV 2PISC # 2PISC (+6) BOV STOREMAX STOREMAX STORE XMAX DMP PDDL 1/ROOTMU ALPHA NORM PDDL X1 SL* DDV 0 -6,1 BOV BMN MODDONE MODDONE # MPAC=PERIOD PERIODCH PDDL ABS # 0D=PERIOD TAU. DSU BMN 0D MODDONE SIGN TAU. STODL TAU. GOTO PERIODCH MODDONE SETPD DLOAD 0 XKEPNEW STORE X SIGN BZE TAU. BADX BMN ABS BADX DSU BPL XMAX BADX STORBNDS DLOAD BPL TAU. STOREMIN DLOAD DCOMP XMAX STODL XMIN KEPZERO STCALL XMAX DXCOMP STOREMIN DLOAD KEPZERO STORE XMIN DXCOMP DLOAD DMPR # Page 1279 TAU. BEE22 ABS STODL EPSILONT XPREV XDIFF BDSU X STORE DELX KEPLOOP DLOAD DSQ X # X=XKEP NORM PUSH # 0D=XSQ (+34 OR +32 -N1) PL AT 2 X1 DMP SRR* ALPHA 0 -6,1 STCALL XI # XI=ALPHA XSQ (+6) DELTIME BOV BDSU TIMEOVFL # UNLIKELY TAU. STORE DELT # DELT=DELINDEP ABS BDSU EPSILONT BPL DLOAD KEPCONVG T DSU NORM TC X1 PDDL NORM DELX X2 XSU,1 DMP X2 DELT SLR* DDV 1,1 SR1 PUSH # 0D=TRIAL DELX PL AT 2 BPL DLOAD POSDELX X STORE XMAX # MOVE MAX BOUND IN BDSU DSU # PL AT 0 XMIN BOV BPL NDXCHNGE NDXCHNGE DLOAD GOTO # Page 1280 0D NEWDELX NDXCHNGE DLOAD DSU XMIN X DMPR GOTO # TO FORCE MPAC +2 TO ZERO DP9/10 NEWDELX POSDELX DLOAD X STORE XMIN # MOVE MIN BOUND IN BDSU DSU # PL AT 0 XMAX BOV BMN PDXCHNGE PDXCHNGE DLOAD 0D NEWDELX STORE DELX BZE DAD KEPCONVG X STODL X T STORE TC BRNCHCTR RTB BHIZ CHECKCTR KEPCONVG GOTO KEPLOOP # ITERATE PDXCHNGE DLOAD DSU XMAX X DMPR GOTO # TO FORCE MPAC +2 TO ZERO DP9/10 NEWDELX BADX DLOAD SR1 XMAX SIGN TAU. STCALL X STORBNDS # Page 1281 TIMEOVFL DLOAD BMN # X WAS TOO BIG X NEGTOVFL STORE XMAX CMNTOVFL DLOAD SR1 DELX STORE DELX BZE BDSU KEPRTN X STODL X TC STCALL T BRNCHCTR NEGTOVFL STCALL XMIN CMNTOVFL KEPCONVG DLOAD SR4R R1 DSU VXSC XSQC(XI) URRECT VSL1 PDDL # 0D=(R1-XSQC(XI))URRECT (+33 OR +31) X DSQ NORM X1 DMPR DMPR 1/ROOTMU X DMP SRR* S(XI) 0 -7,1 BDSU T SL1 VXSC VRECT VSL1 VAD VSL4 STORE RCV # RCV (+29 OR +27) ABVAL NORM X2 STODL RCNORM XI DMPR DSU S(XI) D1/128 DMP SL1R ROOTMU DMP SLR* # Page 1282 X 0 -3,2 DDV VXSC RCNORM URRECT VSL1 PDDL # 0D=URRECT(XI S(XI)-1)X ROOTMU/RCV (+15 XSQC(XI) # OR +13) PL AT 6 SLR* DDV 0 -4,2 RCNORM BDSU VXSC D1/256 VRECT VAD VSL8 STADR # PL AT 0 STODL VCV # VCV (+7 OR +5) T STODL TC X STCALL XPREV KEPRTN # Page 1283 DELTIME EXIT # MPAC=XI (+6), 0D=XSQ (+34 OR +32 -N1) TC POLY DEC 8 2DEC .083333334 2DEC -.266666684 2DEC .406349155 2DEC -.361198675 2DEC .210153242 2DEC -.086221951 2DEC .026268812 2DEC -.006163316 2DEC .001177342 2DEC -.000199055 TC INTPRET STODL S(XI) XI EXIT TC POLY DEC 8 2DEC .031250001 2DEC -.166666719 2DEC .355555413 2DEC -.406347410 2DEC .288962094 2DEC -.140117894 2DEC .049247387 2DEC -.013081923 2DEC .002806389 2DEC -.000529414 TC INTPRET # Page 1284 DMP SRR* # PL AT 0 0D 0 -5,1 STORE XSQC(XI) # XSQC(XI) (+33 OR +31) DMP SL1 KEPC1 RTB PDDL # XCH WITH PL. 0D=C1 XSQ C(XI) (+49 OR +46) TPMODE # PL AT 0,3 DMP SRR* S(XI) 0 -5,1 DMP SL1 KEPC2 RTB PDDL # 3D=C2 XSQ S(XI) (+35 OR +33) PL AT 6 TPMODE R1 SR TAD # PL AT 3 6 NORM DMP # TO PRESERVE SIGNIF. X1 X SR* TAD # X(C2 XSQ S(XI) +R1) (+49 OR +46) PL AT 0 0 -3,1 SL4R DMPR 1/ROOTMU STORE T RVQ # Page 1285 ITERATOR BONCLR DLOAD SLOPESW FIRSTIME DEP DSU NORM DEPREV X1 PDDL NORM DELINDEP X2 XSU,1 DMP X2 DELDEP SLR* DDV # PL UP 2 1,1 SR1 BOFF ORDERSW SGNCHECK ABS SIGN # IN CASE 2ND DERIV. CHANGED SIGN, MUST DELDEP # DISREGARD IT TO FIND MIN. SGNCHECK PUSH BPL # TRIAL DELINDEP PL DOWN 2 POSDEL DLOAD BON INDEP ORDERSW MINCHECK STORE MAX # IF NOT 2ND ORDER, CAN MOVE MAX BOUND IN. MINCHECK BDSU DSU MIN BOV BPL MODNGDEL MODNGDEL GOTO DELOK MODNGDEL DLOAD DSU # TRIAL DELINDEP WOULD EXCEED MIN BOUND MIN INDEP DMP GOTO DP9/10 NEWDEL FIRSTIME DLOAD DMP MIN TWEEKIT # DLOAD TWEEKIT(40D) SENSITIVE TO CHANGE. PDDL DMP # S2(41D) SHOULDN'T CONTAIN HI ORDER ONES # Page 1286 MAX TWEEKIT DSU SIGN GOTO DELDEP SGNCHECK POSDEL DLOAD BON INDEP ORDERSW MAXCHECK STORE MIN # IF NOT 2ND ORDER, CAN MOVE MIN BOUND IN. MAXCHECK BDSU DSU MAX BOV BMN MODPSDEL MODPSDEL DELOK DLOAD 0D NEWDEL STORE DELINDEP RVQ MODPSDEL DLOAD DSU MAX INDEP DMP GOTO DP9/10 NEWDEL CHECKCTR CS ONE INDEX FIXLOC AD ITERCTR INDEX FIXLOC TS ITERCTR TS MPAC TC DANZIG # Page 1287 NEWSTATE DLOAD SR4R R1 DSU VXSC XSQC(XI) UR1 VSL1 PDDL # 0D=(R1-XSQC(XI))UR1 (+33 OR 31) PL AT 6 X DSQ NORM X1 DMPR DMPR 1/ROOTMU X DMP SRR* S(XI) 0 -7,1 BDSU T SL1 VXSC VVEC VSL1 VAD # PL AT 0 VSL4 PUSH ABVAL LAMENTER NORM X1 STODL R2 XI DMP DSU S(XI) D1/128 DMP SL1R ROOTMU DMP SLR* X 0 -3,1 DDV VXSC R2 UR1 VSL1 PDDL # 6D=V2VEC PART (+15 OR 13) PL AT 12 XSQC(XI) SLR* DDV 0 -4,1 R2 BDSU D1/256 VXSC VAD VVEC # PL AT 6 VSL8 RVQ # Page 1288 SETLOC CONICS1 BANK COUNT 04/CONIC # DO NOT DISTURB THE ORDER OF THESE CDS, OVERLAYS HAVE BEEN MADE. BEE17 DEC 0 # KEEP WITH D1/8 2DEC 1.0B-17 (0000004000) D1/8 2DEC 1.0 B-3 D1/128 2DEC 1.0 B-7 D1/64 2DEC 1.0 B-6 D1/4 2DEC 1.0 B-2 D1/16 2DEC 1.0 B-4 D1/32 2DEC 1.0 B-5 D1/1024 2DEC 1.0 B-10 D1/256 2DEC 1.0 B-8 DP9/10 2DEC .9 KEPZERO EQUALS LO6ZEROS -50SC 2DEC -50.0 B-12 2PISC 2DEC 6.28318530 B-6 BEE19 EQUALS D1/32 -1 # 2DEC 1.0 B-19 (00000 01000) BEE22 EQUALS D1/256 -1 # 2DEC 1.0 B-22 (00000 00100) ONEBIT 2DEC 1.0 B-28 COGUPLIM 2DEC .999511597 COGLOLIM 2DEC -.999511597 # Page 1289 SETLOC CONICS BANK COUNT 12/CONIC TIMETHET STQ SETPD # PL AT 0 RTNTT 0 BOV +1 VLOAD PDVL # SETUP FOR PARAM CALL PL AT 6 RVEC VVEC CALL PARAM BOV CALL COGAOVFL # PL AT 0 GETX COMMNOUT DLOAD BON XI INFINFLG ABTCONIC CLEAR CALL COGAFLAG DELTIME BON CALL RVSW RTNTT NEWSTATE GOTO RTNTT COGAOVFL SETGO COGAFLAG ABTCONIC BANK 4 SETLOC CONICS1 BANK COUNT* $$/CONIC PARAM STQ CLEAR # MPAC=V1VEC, 0D=R1VEC PL AT 6 RTNPRM NORMSW CLEAR COGAFLAG SSP CALL GEOMSGN 37777 # GAMMA ALWAYS LESS THAN 180DEG GEOM # MPAC=SNGA (+1), 0D=CSGA (+1) PL AT 2 STODL 36D # 36D=SIN GAMMA (+1) PL AT 0 # Page 1290 SR DDV 5 36D STOVL* COGA MUTABLE,1 STODL 1/MU MAGVEC2 DSQ NORM X1 DMPR DMP 1/MU R1 SRR* 0 -3,1 PUSH BDSU # 0D=R1 V1SQ/MU (+6) PL AT 2 D1/32 STODL R1A # R1A (+6) PL AT 0 DMP NORM 36D X1 DMP SR* 36D 0 -4,1 STCALL P # P (+4) RTNPRM # Page 1291 GEOM UNIT # MPAC=V2VEC, 0D=R1VEC PL AT 6 STODL U2 # U2 (+1) 36D STOVL MAGVEC2 # PL AT 0 UNIT STORE UR1 # UR1 (+1) DOT SL1 U2 PDDL # 0D=CSTH (+1) PL AT 2 36D STOVL R1 # R1 (+29 OR +27) UR1 VXV VSL1 U2 BON SIGN NORMSW HAVENORM GEOMSGN UNIT BOV COLINEAR UNITNORM STODL UN # UN (+1) 36D SIGN RVQ # MPAC=SNTH (+1), 34D=SNTH.SNTH (+2) GEOMSGN COLINEAR VSR1 GOTO UNITNORM HAVENORM ABVAL SIGN GEOMSGN RVQ # MPAC=SNTH (+1), 34D=SNTH.SNTH (+2) # Page 1292 BANK 12 SETLOC CONICS BANK COUNT 12/CONIC GETX AXT,2 SSP # ASSUMES P (+4) IN MPAC 3 S2 1 CLEAR 360SW SQRT PDDL # 0D=SQRT(P) PL AT 2 CSTH SR1 BDSU D1/4 PDDL SRR # PL AT 4D SNTH 6 DDV # PL AT 2 BOV 360CHECK DSU DMP COGA # PL AT 0 SL2R BOV 360CHECK WLOOP PUSH DSQ # 0D=W (+5) PL AT 2 TLOAD PDDL # 2D=WSQ (+10) PL AT 5 MPAC R1A SR4 TAD # PL AT 2 BMN SQRT INFINITY ROUND DAD # PL AT 0D BOV TIX,2 RESETX2 WLOOP BDDV BOV D1/128 INFINITY POLYCOEF BMN PUSH # 0D=1/W (+2) OR 16/W (+6) PL AT 2 INFINITY DSQ NORM DMP X1 R1A SRR* EXIT 0 -10D,1 # Page 1293 TC POLY DEC 5 2DEC .5 2DEC -.166666770 2DEC .100000392 2DEC -.071401086 2DEC .055503292 2DEC -.047264098 2DEC .040694204 TC INTPRET DMP SL1R # PL AT 0D PUSH BON 360SW TRUE360X XCOMMON DSQ NORM X1 DMP SRR* R1A 0 -12D,1 STODL XI # XI (+6) R1 SR1 SQRT ROUND DMP SL4R # PL AT 0 STORE X # X (+17 OR +16) DSQ NORM X1 PDDL DMP # 0D=XSQ (+34 OR +32 -N1) PL AT 2 P R1 SL3 SQRT DMP SL3R COGA STODL KEPC1 R1A BDSU CLEAR D1/64 INFINFLG STORE KEPC2 # Page 1294 RVQ RESETX2 AXT,2 3 360CHECK SETPD BPL 0D INVRSEQN SET 360SW INVRSEQN DLOAD SQRT P PDDL DMP # 0D=SQRT(P) (+2) PL AT 2 SNTH COGA SL1 PDDL # 2D=SNTH COGA (+5) PL AT 4 CSTH SR4 DAD D1/32 DSU DMP # PL AT 2,0 NORM BDDV X1 SNTH SLR* ABS # NOTE: NEAR 360 CASE TREATED DIFFERENTLY 0 -5,1 PUSH DSQ # 0D=1/W (-1) PL AT 2 STODL 34D D1/16 1/WLOOP PUSH DSQ # 2D=G (+4) PL AT 4 RTB PDDL # PL AT 7 TPMODE R1A DMP SR4 34D TAD BMN SQRT # PL AT 4 INFINITY DAD # PL AT 2 TIX,2 NORM 1/WLOOP X1 BDDV SLR* GOTO # PL AT 0 0 -7,1 POLYCOEF # Page 1295 TRUE360X DLOAD BMN R1A INFINITY SQRT NORM X1 BDDV SL* 2PISC 0 -3,1 DSU PUSH # 0D=2PI/SQRT(R1A) -X PL AT 0,2 GOTO XCOMMON INFINITY SETPD BOV # NO SOLUTION EXISTS SINCE CLOSURE THROUGH 0 # INFINITY IS REQUIRED OVFLCLR OVFLCLR SET RVQ INFINFLG # Page 1296 LAMBERT STQ SETPD RTNLAMB 0D BOV +1 SSP VLOAD* ITERCTR 20D MUTABLE,1 STODL 1/MU TDESIRED DMPR BEE19 STORE EPSILONL SET VLOAD SLOPESW R1VEC PDVL CALL # 0D=R1VEC (+29 OR +27) PL AT 6 R2VEC # MPAC=R2VEC (+29 OR +27) GEOM STODL SNTH # 0D=CSTH (+1) PL AT 2 MAGVEC2 NORM PDDL # PL AT 4 X1 R1 SR1 DDV # PL AT 2 SL* PDDL # DXCH WITH 0D, 0D=R1/R2 (+7) PL AT 0,2 0 -6,1 STADR STORE CSTH # CSTH (+1) SR1 BDSU D1/4 STORE 1-CSTH # 1-CSTH (+2) ROUND BZE 360LAMB NORM PDDL # PL AT 4 X1 0D SR1 DDV # PL AT 2 SL* SQRT 0 -3,1 PDDL SR # 2D=SQRT(2R1/R2(1-CSTH)) (+5) PL AT 4 SNTH 6 DDV DAD # PL AT 2 1-CSTH STADR STORE COGAMAX BOV BMN # IF OVFL, COGAMAX=COGUPLIM # Page 1297 UPLIM # IF NEG, USE EVEN IF LT COGLOLIM, SINCE MAXCOGA # THIS WOULD BE RESET IN LAMBLOOP DSU BMN # IF COGAMAX GT COGUPLIM, COGAMAX=COGUPLIM COGUPLIM MAXCOGA # OTHERWISE OK, SO GO TO MAXCOGA UPLIM DLOAD COGUPLIM # COGUPLIM=.999511597 = MAX VALUE OF COGA STORE COGAMAX # NOT CAUSING OVFL IN R1A CALCULATION MAXCOGA DLOAD CSTH SR DSU # PL AT 0 6 STADR STODL CSTH-RHO GEOMSGN BMN DLOAD LOLIM CSTH-RHO SL1 DDV SNTH BOV LOLIM MINCOGA STORE COGAMIN # COGAMIN (+5) BON SSP GUESSW NOGUESS TWEEKIT 00001 DLOAD COGA LAMBLOOP DMP SNTH SR1 DSU CSTH-RHO NORM PDDL # 0D=SNTH COGA-(CSTH-RHO) (+7+C(XI)) PL=2 X1 1-CSTH SL* DDV # 1-CSTH (+2) PL AT 0 0 -9D,1 BMN BZE NEGP NEGP STODL P # P=(1-CSTH)/(SNTH COGA-(CSTH-RHO)) (+4) COGA DSQ DAD D1/1024 NORM DMP X1 # Page 1298 P SR* BDSU 0 -8D,1 D1/32 STODL R1A # R1A=2-P(1+COGA COGA) (+6) P BOV CALL HIENERGY GETX DLOAD T STODL TPREV XI BON CALL INFINFLG NEGP # HAVE EXCEEDED THEORETICAL BOUNDS DELTIME BOV BDSU BIGTIME TDESIRED STORE TERRLAMB ABS BDSU EPSILONL BPL RTB INITV CHECKCTR BHIZ CALL SUFFCHEK ITERATOR DLOAD BZE MPAC SUFFCHEK DAD COGA STCALL COGA LAMBLOOP NEGP DLOAD BPL # IMPOSSIBLE TRAJECTORY DUE TO INACCURATE DCOGA # BOUND CALCULATION. TRY NEW COGA. LOENERGY HIENERGY SETPD DLOAD # HIGH ENERGY TRAJECTORY RESULTED. 0 COGA # IN OVFL OF P OR R1A, OR XI EXCEEDING 50. STORE COGAMIN # THIS IS THE NEW BOUND. COMMONLM DLOAD SR1 DCOGA # Page 1299 STORE DCOGA # USE DCOGA/2 AS DECREMENT BZE BDSU SUFFCHEK COGA STCALL COGA LAMBLOOP BIGTIME DLOAD TPREV STORE T LOENERGY SETPD DLOAD # LOW ENERGY TRAJECTORY RESULTED 0 COGA # IN OVERFLOW OF TIME. STCALL COGAMAX # THIS IS THE NEW BOUND. COMMONLM SUFFCHEK DLOAD ABS TERRLAMB PDDL DMP TDESIRED # PL AT 2D D1/4 DAD DSU # PL AT 0D ONEBIT BPL SETGO INITV SOLNSW RTNLAMB 360LAMB SETPD SETGO # LAMBERT CANNOT HANDLE CSTH=1 0 SOLNSW RTNLAMB NOGUESS SSP DLOAD TWEEKIT 20000 COGAMIN SR1 PDDL # PL AT 2 COGAMAX SR1 DAD STADR # PL AT 0 STORE COGA STCALL DCOGA LAMBLOOP # Page 1300 LOLIM DLOAD GOTO COGLOLIM # COGLOLIM=-.999511597 MINCOGA INITV DLOAD NORM R1 X1 PDDL SR1 # PL AT 2 P DDV # PL AT 0 SL* SQRT 0 -4,1 DMP SL1 ROOTMU PUSH DMP # 0D=VTAN (+7) PL AT 2 COGA SL VXSC 5 UR1 PDDL # XCH WITH 0D PL AT 0,6 VXSC VSL1 UN VXV VAD UR1 # PL AT 0 VSL1 CLEAR SOLNSW STORE VVEC SLOAD BZE VTARGTAG TARGETV GOTO RTNLAMB TARGETV DLOAD CALL MAGVEC2 LAMENTER STCALL VTARGET RTNLAMB # Page 1301 TIMERAD STQ SETPD # PL AT 0 RTNTR 0 BOV +1 VLOAD PDVL # PL AT 6 RVEC VVEC CALL PARAM BOV DLOAD COGAOVFL # PL AT 0 D1/32 DSU DMP R1A P SQRT DMP COGA SL4 VXSC U2 PDDL DSU # PL AT 6 D1/64 R1A VXSC VSU # PL AT 0 UR1 VSL4 UNIT BOV CIRCULAR PDDL NORM # 0D=UNIT(ECC) (+3) PL AT 6 RDESIRED # 35D=ECC (+3) X1 PDDL DMP # PL AT 8 R1 P SL* DDV # PL AT 6 0,1 DSU DDV D1/16 36D # 36D=ECC (+3) STORE COSF BOV DSQ BADR2 BDSU BMN D1/4 BADR2 SQRT SIGN SGNRDOT CLEAR APSESW # Page 1302 TERMNVEC VXSC VSL1 UN VXV PDVL # VXCH WITH 0D PL AT 0,6 0D VXSC VAD # PL AT 0 COSF VSL1 PUSH # 0D=U2 PL AT 6 DOT DDV # LIMITS RESULT TO POSMAX OR NEGMAX UR1 DP1/4 SR1 BOV # SCALE BACK DOWN TO NORMAL +1 # CLEAR OVFIND IF SET STOVL CSTH # CSTH (+1) UR1 VXV VSL1 DOT SL1 UN STODL SNTH # SNTH (+1) P CALL GETX CLRGO SOLNSW COMMNOUT CIRCULAR SETPD SETGO 0 SOLNSW ABTCONIC BADR2 DLOAD SIGN LODPHALF COSF STODL COSF KEPZERO SETGO APSESW TERMNVEC # Page 1303 APSIDES STQ SETPD # PL AT 0 RTNAPSE 0D BOV +1 VLOAD PDVL # PL AT 6 RVEC VVEC CALL PARAM BOV # PL AT 0 GETECC GETECC DMP SL4 R1A BDSU SQRT D1/64 STORE ECC DAD PDDL # PL AT 2 D1/8 R1 DMP SL1 P DDV # PL AT 0 PDDL NORM # 0D=RP (+29 OR +27) PL AT 2 R1A X1 PDDL SL* # PL AT 4 R1 0 -5,1 DDV DSU # PL AT 2,0 BOV BMN INFINAPO INFINAPO GOTO RTNAPSE INFINAPO DLOAD GOTO # RETURNS WITH APOAPSIS IN MPAC, PERIAPSIS LDPOSMAX RTNAPSE # THAT PL IS AT 0. # Page 1304 ABTCONIC EXIT TC P00DOO OCT 00607 # Page 1305 SETLOC CONICS1 BANK COUNT 04/CONIC MUTABLE 2DEC* 3.986032 E10 B-36* # MUE 2DEC* .25087606 E-10 B+34* # 1/MUE 2DEC* 1.99650495 E5 B-18* # SQRT(MUE) 2DEC* .50087529 E-5 B+17* # 1/SQRT(MUE) 2DEC 4.902778 E8 B-30 # MUM 2DEC .203966 E-8 B+28 # 1/MUM 2DEC* 2.21422176 E4 B-15* # SQRT(MUM) 2DEC* .45162595 E-4 B+14* # 1/SQRT(MUM) LDPOSMAX EQUALS LODPMAX # DPPOSMAX IN LOW MEMORY. # ERASABLE ASSIGNMENTS # KEPLER SUBROUTINE # INPUT -- # RRECT ERASE +5 # VRECT ERASE +5 # TAU. ERASE +1 # XKEP ERASE +1 # TC ERASE +1 # XPREV ERASE +1 1/MU EQUALS 14D ROOTMU EQUALS 16D 1/ROOTMU EQUALS 18D # OUTPUT -- # RCV ERASE +5 # VCV ERASE +5 # RC ERASE +1 # XPREV ERASE +1 # DEBRIS -- ALPHA EQUALS 8D XMAX EQUALS 10D # Page 1306 XMIN EQUALS 12D X EQUALS 20D XI EQUALS 24D S(XI) EQUALS 26D XSQC(XI) EQUALS 28D T EQUALS 30D R1 EQUALS 32D KEPC1 EQUALS 34D KEPC2 EQUALS 36D # DELX ERASE +1 # DELT ERASE +1 # URRECT ERASE +5 # RCNORM ERASE +1 # XPREV EQUALS XKEP # LAMBERT SUBROUTINE # # INPUT -- # R1VEC ERASE +5 # R2VEC ERASE +5 # TDESIRED ERASE +1 # GEOMSGN ERASE +0 # GUESSW # 0 IF COGA GUESS AVAILABLE, 1 IF NOT # COGA ERASE +1 # INPUT ONLY IF GUESS IS ZERO. # NORMSW # 0 IF UN TO BE COMPUTED, 1 IF UN INPUT # UN ERASE +5 # ONLY USED IF NORMSW IS 1 # VTARGTAG ERASE +0 # TWEEKIT EQUALS 40D # ONLY USED IF GUESSW IS 0 # OUTPUT -- # VTARGET ERASE +5 # AVAILABLE ONLY IF VTARGTAG IS ZERO. # V1VEC EQUALS MPAC # DEBRIS -- # RTNLAMB ERASE +0 # U2 ERASE +5 # MAGVEC2 ERASE +1 # UR1 ERASE +5 # R1 EQUALS 31D # UN ERASE +5 # SNTH ERASE +1 # CSTH ERASE +1 # 1-CSTH ERASE +1 # CSTH-RHO ERASE +1 COGAMAX EQUALS 14D # CLOBBERS 1/MU COGAMIN EQUALS 8D DCOGA EQUALS 12D # TWEEKIT EQUALS 40D # P ERASE +1 # Page 1307 # COGA ERASE +1 # R1A ERASE +1 # X EQUALS 20D # XSQ EQUALS 22D # XI EQUALS 24D # S(XI) EQUALS 26D # XSQC(XI) EQUALS 28D # T EQUALS 30D # KEPC1 EQUALS 34D # KEPC2 EQUALS 36D # SLOPSW # SOLNSW # OTHERS -- # RVEC EQUALS R1VEC # VVEC ERASE +5 # COGAFLAG # RVSW # INFINFLG # APSESW # 360SW # RTNTT EQUALS RTNLAMB # ECC ERASE +1 # RTNTR EQUALS RTNLAMB # RTNAPSE EQUALS RTNLAMB # R2 EQUALS MAGVEC2 COSF EQUALS 24D # RTNPRM ERASE +0 # SCNRDOT ERASE +0 # RDESIRED ERASE +1 # ITERATOR SUBROUTINE # ORDERSW MAX EQUALS 14D # CLOBBERS 1/MU MIN EQUALS 8D # INDEP ERASE +1 DELINDEP EQUALS 12D ITERCTR EQUALS 22D DEP EQUALS 30D # DELDEP ERASE +1 # DEPREV ERASE +1 TWEEKIT EQUALS 40D # MORE KEPLER # EPSILONT ERASE +1 # Page 1308 # MORE LAMBERT # TERRLAMB EQUALS DELDEP # TPREV EQUALS DEPREV # EPSILONL EQUALS EPSILONT +2 # DOUBLE PRECISION WORD